01 - Preheat oven to 350°F. Grease and flour a 9x5-inch loaf pan, or line with parchment paper for easy removal.
02 - In a medium bowl, thoroughly whisk together the all-purpose flour, baking powder, baking soda, and salt. Set the mixture aside.
03 - In a large mixing bowl, using an electric mixer, beat the softened unsalted butter and granulated sugar together until the mixture is light and fluffy, typically for 2 to 3 minutes.
04 - Add the large eggs one at a time, ensuring each egg is fully incorporated before adding the next. Then, mix in the lemon zest, fresh lemon juice, and vanilla extract until well combined.
05 - Gradually add the prepared flour mixture and whole milk to the wet ingredients, alternating between them. Begin and end with the flour mixture. Mix gently until just combined; avoid overmixing.
06 - Pour the prepared cake batter evenly into the greased and floured 9x5-inch loaf pan, spreading the top smoothly with a spatula.
07 - Bake for 45 to 50 minutes, or until a wooden toothpick inserted into the center of the cake comes out clean. If the top begins to brown too quickly, loosely tent the pan with aluminum foil.
08 - Allow the cake to cool in the loaf pan for 10 minutes before carefully inverting it onto a wire rack. Let it cool completely on the rack before proceeding.
09 - While the cake cools, prepare the lemon glaze by whisking the sifted powdered sugar with 2 to 3 tablespoons of fresh lemon juice until the mixture is smooth and has a pourable consistency. Drizzle the glaze generously over the completely cooled cake. Allow the glaze to set before slicing and serving.